We toss a coin with P(H)=p∈(0,1) indefinitely and independently. You win 2n dollars if on a given run of the coin tosses, H shows up first on the nth toss. Let X be the random variable that gives your winnings for one run of the game. If you play this game repeatedly, what would your expected earnings (e(x)) be? note that depending on the value of p, e(x) can be finite or infinite.